The teleological modal profile and subjunctive background of organic generation and growth

For one of the most natural of works for living things (as many as are complete and not damaged, or not spontaneously generating) is to make another like itself – an animal an animal, a plant a plant – so as to partake so far as it is able in the eternal and divine. … Since, then, it is unable to share in the eternal and divine by way of continuity, because perishable things do not admit of persisting as the same thing and one in number, … it persists not as the same thing but as one like itself, not one in number but one in form.

Aristotle, De Anima, Book II, Chapter 4

Abstract

Formal methods for representing the characteristic features of organic development and growth make it possible to map the large-scale teleological structure of organic activity. This provides a basis for semantically evaluating, or providing a theory of meaning for, talk of organic activity as purposive. For the processes of organic generation and growth are subjunctively robust under a variety of influences characteristic for the kind or species in question, and these subjunctive conditions can be displayed in a two-dimensional array. After motivating and introducing this array, I use its two dimensions to partially account for features of the purposiveness characterizing two sets of exemplars of the plant and animal kingdoms: ferns and cacti, and cheetah and gazelle. The result is a formal framework for interpreting talk of organic activity as purposive, able to be adapted to a range of research traditions in the philosophy of language and the philosophy of biology.

1 Introduction and motivation

Work on this paper was supported by the Czech Science Foundation, Grant No. 20-05180X, at the Faculty of Philosophy, University of Hradec Králové. These ideas first came together while I was writing my dissertation. My thanks to Robert Brandom, Edouard Machery, John McDowell, and Jim O’Shea for discussion during that period. I am also indebted to conversation with participants at the “(Re)Conceptualizing Function and Goal-Directedness” cluster meeting for the project Agency, Directionality, and Function, held at the University of Reading, September 12-16, 2023. Finally, thanks are owed to Fermín Fulda, Daniel McShea and three reviewers for this journal, each of which gave extensive and very helpful comments on the essay.

Despite growing interest in teleology across the philosophy of language (Millikan, 1984; Macdonald & Papineau, 2006; Nanay, 2014; Papineau, 2017), metaphysics (Ben-Menahem, 2018; Illetterati & Michelini, 2008; Page, 2021; Sehon, 2005), the philosophy of mind (Perner & Roessler, 2010; Popa, 2021), and the philosophy of biology (Allen & Neal, 2020; Garson & Papineau, 2019; Lee & McShea, 2020; McShea, 2012; Moreno & Massio, 2015; Walsh, 2008), little attention has so far been paid to the formal structure of teleological reasoning. This is surprising, given (1) the attention paid to modal and intensional language in philosophy and linguistics over the last century, and (2) the range of teleological vocabularies present in natural language, which in English include the two-place connectives so that and in order to, evaluative terms like good and defective, and functional expressions (denoting processes or activities) like is Xing for Y.

At the center of this essay is a formalism, presented as a two-dimensional array of subjunctive conditionals, where the relations defined across this array are used to explain features of teleological talk about complex organic activity of the sort found in the development (or genesis via reproduction) and growth of multicellular organisms (most of the examples involve plants). My focus lies on subjunctive conditionals, marked by talk of what would be the case were something to happen, rather than what grammarians call the subjunctive mood, which is used to convey one’s wishes, desires, or suggestions (and for my purposes here, I treat counterfactual conditionals as a kind of subjunctive). Schematically, subjunctives will be displayed with the wedge, and sentences with either Greek or English letters, as in φ > ψ (this can be read as “if it were to be that φ, then it would be that ψ”, although in the exposition I tend to speak in less regimented terms). In the process of laying out this formalism, I explain how its features account for (our thought and talk about) the activities typical of organic things as tending toward their survival and reproduction, and their diversity in the different kinds of purposive flourishing found in the organic world. Doing so helps explain both the cognitive role or semantic function of a class of teleological modal claims concerning organic development and growth, and our understanding of organisms as the kinds of thing they are.²

The focus here lies on what is characteristic of paradigmatic cases of organic purpose, in that the target of inquiry is the general form of organic teleology, understood through a linguistic model of our talk of organic things as purposive. The claims made with such talk exhibit an intensionality similar to that of characterizing generics like “summers in Greece are warm” and “mosquitos carry malaria”: their use communicates something about the members of the kind that does not depend on all (or any particular number) having the property in question. Similarly, plants grow in the directions they do so that they can reach sunlight, and sperm are produced in order for the animal to reproduce, despite the fact that some or most of the things in question do not achieve these ends. Use of these claims communicates features about the kind that are characteristic or otherwise relevant to our thought about the members of that kind (see Stovall 2023a for an analysis of characterizing generics consonant with the view developed here).

My lexical target is the two-place teleological modal operator “so that”, interpreted as taking sentences in its two positions, as in “φ so that ψ”. In the language of Wright (1976) and Nagel (1977a), my interest lies in teleological or functional explanations about living things, like “fish have gills so that they may respire”, rather than ascriptions of purpose to organic parts or activities, as in “the purpose of gills in fish is respiration”. But in exposition of the view, I make use of a range of teleological, functional, and normative vocabularies, and I regularly use teleological language to ascribe purposes to organisms. I do so in order to call to mind both the naturalness with which we give and accept teleological assertions about organic activity, and to highlight some of the ways our acceptance of these assertions coordinates our thought about the living world.

The relationship between teleological judgments and explanation is discussed over the next three sections, but the idea that teleological claims about the organic world figure in explanations for why organisms behave as they do—and thereby account for at least some of our understanding of the organic world—is widely acknowledged in the literature on biological teleology (see, e.g., Ayala, 1998; DiFrisco, 2019; Fulda, 2020; Nagel, 1977a; Uller, 2023; Walsh, 2012, 2013 and Wright, 1976). I extend this research by showing that teleological language about organic purposes can be understood as a means for communicating details about the spatio-temporal tendencies characteristic of organic activity, organized by arrays of subjunctive conditionals with a specific two-dimensional structure. Over the course of the first half of the essay, I argue that our grasp of this structure, to whatever extent we can, enables us to (1) reason about the behavior of organisms in various situations, and so (2) track organisms through space and time as the determinate things they are. The second half of the essay presents that two-dimensional array, discusses its structure, and illustrates how various features of organic development and growth can be explained in terms of it.

The philosophical context is sufficiently complex as to require some care in developing it. But reflection on prosaic features of living things easily motivates the suggestion that our thought about the organic world is governed by reasoning of the sort marked by teleological claims, and underwritten by subjunctively stable relations typical for the kind of organism in question. Consider a pepper plant growing from seed in a garden over the course of a typical midwestern U.S. summer, and imagine the various influences the typical environment will have on the plant over that time. As insoluble starches in the seed are catalyzed into soluble sugars capable of use in growth, two slender tendrils emerge from the seed body: the shoot and root apical meristems, the former rising toward the sun and the latter into the earth. In each meristem, new structures are built to harness the opportunities afforded by the environment for the plant’s further development. Alternating bouts of rain and sunshine fuel the plant’s growth as it draws nutrients from the environment (such as CO₂), uses solar and electrochemical energy to break these nutrients down into simpler molecular components (such as carbon drawn from CO₂), and recombines those components into the sundry materials needed for its subsequent growth. Its roots also serve to anchor it in place, protecting it against the impact of disturbances that would tend to uproot it. Insect attacks will be warded off with the release of toxins, and other enzymes will spur the release of adenosine triphosphate (ATP) at the site of an injury so as to fuel the production of cellulose to seal the wound. Should a squash plant grow nearby, whose leaves threaten to crowd out the sun, this would induce the pepper plant to branch its leaves away from the squash in order to reach sunlight. Given a fortuitous place in an environment suitable for pepper plants, these activities tend toward the plant’s flourishing as the specific kind of plant it is. If all goes well, the plant will flower and produce its fruit. In this way, a new generation of pepper plants is made possible (even likely, again if all goes well).

Notice that nothing important turns on the biochemical details of the plant’s behavior. A pepper plant whose sunlight is crowded out will adjust its daily photosynthetic activity to increase the rate of light capture relative to carbon fixation during the time when light is available, and this may involve long-term changes in the plant’s development—a complex protein- and gene-regulated pathway (see the discussion of the model plant Arabidopsis thaliana, thale or mouse-ear cress, in Waters and Langdale 2009, p. 2869). But a gardener need not know any of this to see that a pepper plant will need to adapt to its condition if placed too close to a squash. Biochemistry allows for a more precise characterization of these processes than was available to pre-scientific cultures, enabling our more fine-grained discernment of the processes that mediate development and growth, but the large-scale subjunctive tendencies of the plant’s activity were in some measure understood without that discernment. Even without comprehending the intermediate means by which the plant’s ends are realized, we recognize its ends as the ends they are by subsuming them under a conception of the plant as a specific kind of organism. In so doing, we think of the pepper plant as an organism whose flourishing is specified in terms of these ends.

Explicit teleological characterizations of the activities of the organism come readily to mind, and we often embed other modalities within these teleological contexts. The plant will grow toward the sun so that photosynthesis can occur; the mitochondria must release ATP in order for the wound to be healed; the plant produces fruit so that the individual can reproduce. The alethic and temporal modalities within these teleological claims mark out the various ways the satisfaction of an organism’s purposes are related to other things in space and time—the will of the first indicates that growth toward the sun can be expected given the way things currently stand, while the must of the second claim indicates the stronger condition that there is no closing of a wound without ATP, and the can in the third indicates that the production of fruit does not of itself guarantee reproduction.

Talk about an organism’s purposes can be interpreted as a means of communicating large-scale patterns of subjunctive robustness—tendencies toward various outcomes even in the presence of potential defeaters—that recur across organic activity. Just so, given a suitably rich understanding of the background conditions obtaining at a context of utterance, to say “the pepper plant is growing out from under the squash in order to reach sunlight” is to convey or otherwise stake a claim on the subjunctive robustness of the tendency of the plant’s growth to be toward the sun. When said to another, it offers them an explanation for what the plant is doing, by providing them a point of orientation concerning (what can be inferred about) the plant’s behavior. For the gardener, it counsels giving the squash plant more room to grow next season.

At the same time, such talk can be understood as limning (or at least purporting to limn) the mind-independent structure of organic activity as the spatio-temporal phenomenon it is. That is to say, while the discussion here is primarily phrased in terms of a reflective stance on the way we speak and think about organic activity, it is also directed, through that reflection, on representing facts about organisms as the kinds of things they are. In the following section, I situate this proposal in the context of different positions on the semantic evaluation of modal vocabulary. In doing so, I indicate how the view might be integrated with a number of model-theoretic and proof-theoretic interpretations of the subjunctive conditional. This is meant to allow for a dual or joint reading of teleological and subjunctive modal claims both as representations of the way things are, and as expressions of the way we reason. In Sect. 3, I consider the proposal alongside ongoing debates about teleological claims in the philosophy of biology. Section 4 argues that our understanding of spatio-temporal objects as members of kinds is conditioned by our understanding of the spaces of subjunctive possibility typical of those kinds. Readers familiar with the literature discussed in Sects. 2, 3, and 4 can skim these sections, as the positive proposal begins in Sect. 5 (but note well the discussion of subjunctive backgrounds and subjunctive stabilities at the end of Sect. 4).

In Sect. 5, I discuss some of the features of organic generation and growth emblematic of its purposiveness, closing with a list of five desiderata that a subjunctive account of these features can be expected to satisfy. Section 6 introduces a two-dimensional array of subjunctive conditionals, concerning the parts of an organism and their interactions with one another. In Sect. 7, I show how that array can account for the desiderata listed in Sect. 5. As an illustration, in Sect. 8 I use these two dimensions of subjunctive structure to explain features of the purposive lives of ferns and cacti, closing with a brief application of the view to the development of visual systems in cheetah and gazelle. The result is (1) a formally tractable and straightforward extension of any of a range of model-theoretic and proof-theoretic semantic interpretations of the subjunctive conditional, to an expanded language including at least some kinds of teleological modal operators, and (2) an explanation as to the aptness of teleological language for characteristic (that is, paradigmatic or generic) processes of organic generation and growth, spelled out in terms of structural features of the formalism. Toward this end, the formalism is presented as a common framework suitable for use across otherwise divergent research programs, and at the close of the essay I indicate how it might be used to predict the presence of organic purposiveness in what may otherwise seem to be non-organic systems.

2 Logical and linguistic background

Whereas the teleological modalities have received comparatively little attention over the last century, the semantics of the subjunctive conditional has been extensively studied, following the modal revolution in philosophy and linguistics that took place in the middle of the twentieth century. Typically, subjunctive conditionals are understood in terms of truth conditions and possible worlds: very roughly, a subjunctive is true at a world just in case all of the most similar worlds at which the antecedent is true are also worlds at which the consequent is true (as in Lewis, 1973 and Stalnaker, 1968). The pioneering work of Lewis and Stalnaker on subjunctive conditionals came together during a time when Montague (overlapping with Lewis at UCLA) developed a typed possible-world semantics sufficient to formalize wide swaths of the syntax of natural language in terms of its surface grammar (see Partee, 2011 and Schiffer, 2015). Prior to this breakthrough, natural language surface grammar was widely regarded as a poor guide to semantic meaning. By showing that a theory of types could be used to systematically translate between surface grammar and formal calculi of the sort philosophers and logicians had been using for decades, Montague’s program allowed for the systematic application of those calculi to natural languages.

With the subsequent development of formal linguistics and the 1970s and ’80s (e.g. in the work on conditionals and modality by Kratzer, 1979, 1986), possible-world model theories for linguistic meaning would become, by the 1990s, regularly presumed given as common ground across much of the philosophy of language, linguistics, and metaphysics (as evident in textbooks for formal semantics like Jacobson, 2014, Portner, 2005, and Winter, 2016). In the interest of generality, the account here is framed so as to be capable of integration with a variety of model-theoretic and representational analyses of the subjunctive conditional, of the sort typified by possible-world semantics (see Divers, 2002 for an overview).³

This account is also meant to permit integration with inferential or proof-theoretic semantics.⁴ The inferentialist proposes that the semantics of various linguistic items should be understood not in terms of worldly conditions specified by a truth-conditional or representational interpretation laid down in a model, but rather in terms of the rules that govern the use of those devices in conversation about the reasons one has to say and do what one does. In the proof-theoretic tradition in logic and mathematics, pre-eminent among these meaning-conferring rules of inference are the introduction and elimination rules specified by a proof system. Such systems lay down rules for inferring to an expression (via an introduction rule) as the conclusion of an inference, and from that expression (via an elimination rule) as a premise in an inference. A proof system’s introduction and elimination rules thereby define different classes of inference that expressions figure into, and those inferences can in turn be used for specifying the semantic interpretations of different object-language lexical items: rules of inference are meaning-conferring for different classes of vocabulary.

A foundational text in the inferentialist tradition, and one that concerns the interpretation of the subjunctive conditional, is Wilfrid Sellars’ “Inference and Meaning” (1953). In that essay, Sellars proposes that object-language subjunctive claims be understood in terms of a metalanguage of material rules of inference—rules concerning the use of non-logical vocabulary. In doing so Sellars extends a program, laid out in Carnap’s The Logical Syntax of Language (2002; first published in German in 1934 and English in 1937), for using a syntactic metalanguage to interpret object-language intensional and metaphysical vocabularies. On the view Sellars defends, the object-language assertion of a subjunctive conditional like “if the cup were tipped over, the water would spill out” is to be understood as a means of conveying or expressing commitment to a material rule of inference from “the cup is tipped over” to “the water spills out”. This inference is material in that its goodness is explained in terms of what water is, and the way it behaves when in a cup tipped over.

Formal features of the subjunctive conditional, and of material rules of inference, support this analysis. For the subjunctive conditional is intensional, inasmuch as the truth of a subjunctive does not depend upon the truth of the sentences in it. Just so, the rule for antecedent strengthening (from “if φ, then ψ” one can infer “if φ and χ, then ψ”) does not in general hold for the subjunctive conditional: to revert to a language of facts and their implications (and so to use the language that was mentioned in discussing material inferences at the end of the last paragraph), from the fact that water would spill out if the cup were tipped over, it does not follow that if the cup were tipped over after having been frozen then water would spill out. And just as subjunctives fail antecedent strengthening, so are material inferences defeasible. The fact that there’s a context-sensitive good inference from “the cup is tipped over” to “the water spills out” doesn’t entail that such an inference remains good after adding the premise “the cup is frozen” to the premise set. Sellars’ insight was to see that our tracking these regions of material-inferential relation, however fallibly we do, is a condition on our understanding—or meaningfully talking about—such things as cups filled with water.⁵ Material inferences, and the subjunctive conditionals we use to express them, articulate our understanding of and cognitive grip on things.

I develop this point more carefully in Sect. 4, when considering the role played by species or kind concepts in our understanding of the world. For now, it is enough to indicate that Sellars’ proposal for the subjunctive conditional might be generalized to other intensional or modal vocabularies. The alethic modalities for necessity and possibility, for instance, might be understood in terms of quantifications over the antecedents of subjunctive conditionals (see chapter 3 of Stovall, 2015a for one such analysis):

$$\begin{aligned} \square \upvarphi \, =_{{{\text{def}}.}} (\forall {\text{p}})\left( {{\text{p }} > \, \upvarphi } \right) \hfill \\ \diamondsuit \upvarphi \, =_{{{\text{def}}.}} (\exists {\text{p}})\left( {{\text{p }} > \, \upvarphi } \right) \hfill \\ \end{aligned}$$

On this proposal, talk of necessity is talk of what would be the case no matter what, while talk of possibility is talk of what would occur if some condition were met. On a material-inferential interpretation of the subjunctive conditional, talk of what is necessary and possible might then be understood as a mechanism for coordinating common ground concerning those inferences that are foreclosed and those which remain open at some point in a conversation. Taking this proposal one step further, intensional talk adverting to organic purposes might be understood as a means for communicating features of a material-inferential proof system, one which governs our understanding of living things. For where our understanding of organic activity is a matter of accurately representing the way organic things behave, such a material-inferential proof system can be understood as one that encodes facts about the organic world.

A joint proof-theoretic material-inferential and model-theoretic representational account of the semantic function of teleological modality might seem difficult to make sense of today. After all, representational and inferential theories of meaning are frequently pitted against one another. But prior to Carnap’s ushering in of what would come to be called “possible-world semantics” in Meaning and Necessity (1947), it was common to treat meaning as having two complementary dimensions: one notion denotational and concerning concept-world relations, and the other a connotational, reflexive, or intraconceptual dimension of meaning. In other work, I have begun to use the resources of model theory and proof theory to develop joint denotational (or representational) and connotational (or inferential) theories of meaning for different kinds of vocabularies (2021, 2022a, 2022b, 2022c, 2023a, 2023b). This is an extensive project, by no means complete, and the current essay contributes to a portion of it. But that background is not necessary for the view presented here, which is constructed so as to be compatible with any of a number of either inferential/proof-theoretic or representational/model-theoretic interpretations of cognitive-linguistic meaning.

On account of these background commitments, in what follows I help myself both to ontic talk of the way things would and would not be, of organic purposes, ends, goals, values, etc., and to nominalized talk of meanings, notions, thoughts, ideas, etc., where this should be understood in terms of a deontic metalanguage of material rules of inference. Readers who incline to semantic monovision along one or the other of these dimensions are free to dispense with either frame (though perhaps at the cost of not appreciating the binocular perspective of the view). My interest here lies in, as it were, looking “out” at the teleological modal semantic structure of organic activity available from this stance, rather than “in” at the semantics and metaphysics of subjunctive conditionals, material inferences, and possible worlds it presupposes—and regardless of whether the emphasis is placed, in that “inner” register, on model-theoretic worldly conditions of truth or proof-theoretic intralinguistic rules of use.

3 Background in the philosophy of biology

The commitments adopted in this essay are also meant to be compatible with a range of positions on teleological language in the philosophy of biology, and to offer a common framework for the further investigation of these positions.

In the literature on teleological explanations in biology, it is common to distinguish causal-history (or etiological) and causal-role accounts of biological purposes (see Okasha, 2019, chapter 3, for an overview). Causal-historical/etiological accounts (e.g. in Neander, 1991) are directed at explaining why an organic trait has the purpose(s) it does, while causal-role accounts (e.g. Cummins, 1975) explain how some organic trait works. While it is true that the pepper plant’s growth toward the sun is explained by features of the causal-historical background of the evolution of that trait in the species, an account of what is expressed by teleological talk, of the sort given here, need not appeal to causal-historical background. For awareness of that causal history is not necessary for understanding at least some of the subjunctive structure communicated by talk of the plant’s growth as purposive. So long as one knows enough about gardening, and about the garden in question, upon being told “the pepper plant is growing out from under the squash in order to reach sunlight” one can infer quite a bit about how the plant would behave in situations that obstructed its access to the sunlight. This suggests that such talk might be reconstructed along a causal-role line of analysis, but I refrain from doing so here.

Another point of debate concerns whether talk of organic purposes should be given a realist or an instrumentalist gloss. For the realist, teleological language should be understood as representing facts about organisms, perhaps marking them as a distinct kind of entity, while for the instrumentalist teleological language is a useful heuristic or methodological commitment that carries no (or little) ontological or metaphysical significance. Recent defenses of realism include the neo-Aristotelian views of Walsh (2006) and (2012), and Fulda (2017). Desmond and Huneman (2020) argue for a neo-Kantian approach, on which teleological talk about organisms is indispensable (a condition on the possibility of understanding the organic world) but non-ontic. This is contrasted with Walsh’s Aristotelian position, on which such talk is both explanatorily indispensable and ontic. The vitalism defended in Walsh (2018), however, is a methodological commitment rather than an ontological one; it concerns our need for the right concepts required to understand organisms as the things they (metaphysically) are. From p.167:

The metaphysical position is that organisms constitute a special category of entity; they are natural agents. The methodological proposal is that, because organisms are agents, a genuine understanding of the difference they make to the world requires a battery of theoretical concepts and explanatory modes that do not apply to the study of non-living things.

Meanwhile, Corti (2022) argues that Hegel inherits a broadly Kantian view on the organism, and he illustrates how organizational accounts of organisms in the philosophy of biology, of the sort defended in Bich et al. (2016), Moreno and Mossio (2015), and Mossio et al. (2009), help illuminate Hegel’s view.

One concern with realism is that it may lead to thinking of unicellular organisms and plants as minded things.⁶ Instrumentalism is one way of avoiding this conclusion; another is to reduce the ontology of organisms to some variety of mechanism. Addressing this concern, Fulda (2017 and 2020) strikes a middle path between mechanistic reductions of organic agency to non-teleologically conceived biology, and Cartesian conceptions of agency as everywhere-and-always minded. This amounts to a defense of the claim (2020, p. 316, note 1) “that what is required is neither a biological reformulation of cognition nor extending the domain of psychology to biology, but the articulation of a distinctive concept of biological agency in the conceptual space between cognition and mechanism.” Fulda’s approach can be understood as an effort in theory-construction. By contrast, in the interest of avoiding such debates McShea writes (2016b, p. 93):

[P]roviding necessary and sufficient conditions for teleology is not the mission here. This is not a project in analytical philosophy. It is not an explication of our usage of a term. Rather, it is an engineering analysis, in the style of Wimsatt (2007), intended to reveal how seemingly teleological systems actually work.

This quick survey indicates some of the ongoing discussion about the metaphysical and explanatory commitments consequent on talk of organic teleology. The view here is framed without coming down too strongly in favor of any one position over another.

As with Fulda’s, my analysis can be understood as articulating a structure specific to organic generation and growth. And as with McShea’s, the approach eschews an interest in necessary and sufficient conditions. Instead, it examines the kinds of cognition characteristically (though not universally) involved in talk of organic purposes. But as a project in analytical philosophy, pace McShea I propose to explicate our usage of teleological modal operators.⁷ And although the account does not foreclose instrumentalist readings, there is at least the following sense in which teleological judgments about organisms typically represent teleological facts about the world. Whereas chemical and mechanical things are like organisms in that they may come into and pass out of existence, the flourishing and perishing of a paradigmatic instance of an organism is of a different sort of order. Contrast the subjunctive relations characteristic of the pepper plant’s interaction with its environment, as against the effect of summer weather on a bag of charcoal. The environment degrades the latter and leads to the flourishing of the former. And while the charcoal would sustain a sizable flame for a while if ignited, the possibilities bound up in the charcoal are, in terms of their relationship to the bag as the sort of thing it is, of a different kind. In this regard, the view is neo-Aristotelian: the subjunctive structure that needs to be tracked in order to understand organic activity is not an artifact of our thought; it is a feature of the world that our thought, if we are to recognize an organism as that kind of thing, must make itself responsible to (which is not deny the possibility that purposive and non-purposive activity lie on a continuum or admit of degrees, as discussed in Sect. 7 below).

All the same, the view has a recognizably Kantian element as well, insofar as it is founded on a reflective articulation of our cognition about the organic world, as manifest in the use of teleological modal vocabulary, and only indirectly on the metaphysics of organisms. I claim to exhibit some of the subjunctive structure, the material-inferential space evident in our talk, of living things and processes. But the aim is not to analyze purposes in terms of subjunctives, understood metaphysically: it is rather to understand our talk of purposes in terms of the subjunctives expressed by that talk.

More specifically, my claim is that we can understand teleological talk about organic activity as an expression of commitment to patterns of reasoning marked by structures in the two-dimensional arrays of subjunctive conditionals introduced below. To the extent this analysis tracks facts about the spaces of possibility that delimit the organic thing, it can be said to offer a metaphysics of the organic world. In that regard, the project is a neo-Aristotelian one. But that metaphysics is read off of the cognitive states expressed by the use of teleological vocabulary, and for this reason it can also be regarded as a neo-Kantian one. Finally, because I do not stake out a position on whether this is a metaphysics we should adopt, but instead aim to illustrate what our ordinary thought and talk already commits us to by way of a metaphysics of the living world, this is a project in descriptive rather than prescriptive metaphysics (see Strawson, 1959 for this distinction).

4 Kind terms, criteria of understanding, and the subjunctive backgrounds of spatio-temporal objects

Although this discussion presupposes the notion of an individual organism, as well as the notion of an organism’s kind or species, each presupposition has received extensive criticism in the literature on biological teleology.⁸ Rather than address whether and on what basis a division of organisms into individuals and their species can be given, I presume a familiar grip on organic development and growth—of the sort humans have had to acquire as we turned to agriculture and animal husbandry for survival—in the interest of illustrating some of the structural details of this familiarity.

This presumption is not ungrounded. As a matter of fact, human beings have been classifying organisms into empirically informed kinds for millennia, and the role of kind terms in facilitating the practical and theoretical grasp of individuals has received widespread attention in analytic philosophy for well over a century. In the Foundations of Arithmetic, first published in 1884, Frege argued that a term can be used to say something about an object only insofar as that use is associated with criteria for numerically individuating the object as a singular thing distinct from other things—criteria of identity and individuation.

If we are to use the symbol a to signify (bezeichnen) an object, we must have a criterion for deciding in all cases whether b is the same as a, even if it is not always in our power to apply this criterion. (1950, §62)

Frege’s discussion of this issue was circumscribed by his interest in fixing, in general, the value of phrases of the form “the number of Ks”. In any specific case, to fix that value is to count things of the kind K, and it is here that criteria of identity and individuation are needed. For to count Ks one must know what it takes to be a K, and without criteria of membership in a kind the process of counting cannot occur. The question “how many things are in the car?” does not have a settled answer unless some sortal or kind is in play (perhaps implicit given the context—e.g., packing for a vacation). Dummy-kinds like thing will not suffice: Is the shadow from the steering wheel a thing? Is the shadow at two different times two different things? What about the spatio-temporal trails of the dust motes? What of their parts?

While Frege was interested in the specific task of counting, the more general practice that underlies the ability to count is the numerical individuation of objects, and correlatively the use of symbols to refer to them. Analytic philosophers in the second half of the twentieth century devoted considerable effort toward understanding, on the one hand, the relationship between the use of terms and sentences to make claims about objects; and on the other, the criteria of identity and individuation (associated with kind terms or sortals) that make reference to individuals possible.⁹ Michael Dummett, Peter Geach, E. J. Lowe, W. V. O. Quine, Peter Strawson, David Wiggins, and Timothy Williamson each made substantial contributions to this debate, often in dialogue with one another, and these discussions have spawned a sizable secondary literature.¹⁰ Here is Wiggins (2001,  p. 18, emphasis in the original; compare with Geach (1980, pp. 63–64), and Lowe (2009, pp. 67–68)—the first editions of these three books date to, respectively, 1980, 1962, and 1989):

The practical grasp of identity itself presupposes the capacity to subsume things under kinds, to refer to them and to trace them (or keep track of them). But in order to trace things, one has to trace them in the way that is appropriate to this or that kind…

While there is much that remains contested in these debates, it is near common ground that even where criteria of identity and individuation cannot be given explicit formulation, our facility with the classification of individuals under kinds presupposes an implicit grasp of those criteria: compare Wiggins’ talk of our “irreducibly practical understanding of ‘the same f’” (2001, p. 104; cf. p.7), with Williamson’s gloss on the requirement that “an approximate criterion of identity should be implicit in the subject’s practice, even if the subject cannot make it explicit” (1990, pp. 152–153), along with Lowe’s dialogical or social-practice account (1989, p. 20):

Nor should we expect ordinary unreflective language-users to be able to articulate explicitly the criteria governing their use of a sortal like “ship”: their implicit application of criteria may be discerned in their ability to respond in principled ways to appropriate questions concerning the identity or persistence of ships subjected to various sorts of changes.

Framed in dialogical terms, the ability to trace persistence conditions for spatio-temporal objects requires being able to say something about how objects of that kind would and would not behave in different environments. Dispositional predicates like flammable and brittle go shorthand for this capacity to track objects across these spaces of environmental possibility, and in relation to other objects and processes. To be told the box is flammable is to be in a position to draw new inferences about how that box would behave when exposed to flame. Use of subjunctives and disposition predicates gives public expression to this world-regarding practice of drawing (and being disposed to draw) inferences. Just so, talk of a stone as brittle, a box as flammable, or a cup as liable to spill water, is talk that communicates to a listener something about the conditions under which a stone, a box, or a cup of water would and would not do various things (at the limit, pass out of existence).¹¹

More generally, the cognitive grip one has on an object in space and time requires individuating that object against a background of merely possible spatio-temporal events—which need not be an all-or-nothing affair, as Lowe and Williamson point out.¹² This individuation proceeds by way of understanding how objects of that kind tend to behave in various situations. This conception is facilitated by the use of dispositional predicates, and by the rules of inference associated with kind terms, which must include not only criteria of identity and individuation, but also criteria of understanding or application. Grasp of criteria of identity and individuation allow one to specify when some member of a kind K is the same as some other member of K—in a proof-theoretic metalanguage, they specify rules for using “is the same K as”. Criteria of understanding or application, on the other hand, allow one to specify what entitles one to classify something as a K, and what follow from that classification. In a nominalized proof-theoretic metalanguage, criteria of understanding can be thought of as material introduction and elimination rules, specifying the context-relative inferences that can be drawn from and to the use of different kind terms.¹³

That these two sets of criteria can come apart is evident from a couple of considerations. On the one hand, some terms carry only criteria of application and no criteria of identity and individuation. Non-sortal adjectival expressions like “red” and “happy” can be correctly and incorrectly applied, but it makes no sense to say “is this the same red as that”, save that an implicit sortalizing expression like “shade of red” is meant. On the other hand, criteria of application can vary across kind terms associated with common criteria of identity and individuation. The terms “politician” and “doctor” have different criteria of application, but insofar as both refer to kinds of human social life, they share the criteria of identity and individuation associated with the kind term “human being”. To count politicians or doctors is to count human beings, and for a politician or doctor to be numerically identical with someone else is for the person in question to be the same human being. Similarly, one might be perfectly adept at counting chimpanzees and bonobos, and so have a grasp of the associated criteria of identity and individuation, without having much understanding of the more specific kinds of primates that bonobos and chimpanzees are (for more on this distinction, see pp. 217–230 of Brandom, 2015, chapter 16 of Dummett, 1981, and Sect. 4 of Noonan & Curtis, 2022).

In an ontological rather than deontic register, these two sets of criteria might be understood in terms of the space of possibility “surrounding” some object as the object’s subjunctive background, grasp of which is a condition on counting members of the kind (with criteria of identity and individuation) and understanding objects of that kind (with criteria of application) For some purposes, the subjunctive background of an object might be represented as a phase space of spatio-temporal coordinates, together with an ontology whose elements are specified as obtaining or not at every coordinate, and a relation of subjunctive or temporal succession defined over that space. This way of formalizing the subjunctive background for an object might be useful in building simple models of the sort Lee and McShea (2020) construct for operationalizing goal-directedness, and it recommends the branching-times modal semantics of Belnap et al. (2001), but I shall continue to speak in general model-theoretic-cum-proof-theoretic terms.

Large-scale features in the subjunctive background of an object are often particularly important for understanding general classes or kinds of thing. An unsupported middle-sized object released near the surface of the earth, for instance, would fall toward the surface of the earth. This tendency is subjunctively robust in that, for a variety of antecedent conditions φ, an unsupported middle-sized object would fall toward the earth were φ to occur. Awareness of this feature of unsupported middle-sized objects is an important condition on understanding them (which is not to deny that it may also be important for identifying and individuating such objects as well). Call a property or relation of an object subjunctively stable when the possession of that property or relation is subjunctively robust under a variety of antecedent conditions (this is of course a general characterization and not a definition, and it allows that different degrees of robustness might be required for the aptness of such talk in different contexts). I will also nominalize talk of properties and relations and speak of subjunctive stabilities directly.

Different kinds of objects bear different kinds of structure in the subjunctive stabilities found in their subjunctive backgrounds. The tendency of an unsupported object to fall toward the surface of the earth is not much affected by different antecedent conditions in most contexts of relevance to us, nor is it a tendency that requires much consideration of the more specific kind of object that falls, or the ways its falling would remain stable under variations in the environment (though of course there are exceptions). And a marble rolling around the inside rim of a bowl to gradually rest at the bottom would return to that trajectory after any number of slightly different gentle disturbances. But the characteristic activity of a growing organism involves subjunctively stable relations among the organism’s parts, and toward the ends typical of those kinds of organism. These subjunctive stabilities sweep out a pattern across the space of possibility that is characteristic of the flourishing of the kind. In order to understand these specific kinds of flourishing, we must draw on the specific kinds of reasoning characteristic of teleological language.

In the philosophy of biology, this is a point agreed on across perspectives as different as Walsh’s neo-Aristotelian account of organic purposes, and Desmond and Huneman’s neo-Kantian one. For Desmond and Huneman (2020), teleological explanations of the organic world are a “demand of reason”, and scientifically indispensable (pp. 35–36). In treating teleological claims as explanations, Walsh (2012) argues that such explanations must involve an elucidating description which “enhances our understanding of the phenomenon to be explained” (p. 175). DiFrisco (2019), meanwhile, argues that biological individuals are countable instances of biological kinds, and he uses different sorts of explanation to individuate different kinds of organic individual, counseling pluralism about the kinds of organic individual we countenance in our theories.¹⁴ It is also not uncommon to see explanation and the individuation of organisms characterized in subjunctive terms. Nagel (1977b), for instance, speaks of goal-directed processes in terms of subjunctive conditions (e.g. at p. 273), while in (1977a) he argues that talk of functions in biology can be explanatory: to specify a trait’s function is to explain something about the organism’s welfare. Fulda (2017) ties the explanatory value of teleological talk about bacterial movement to the fact that such talk underwrites subjunctively (or counterfactually) robust claims about future movement, and his account of goal-directed systems is framed in terms of this robustness (p. 84). From p. 72:

Because of this robust counterfactual dependence between means and goals, knowing the bacterium’s goal allows us reliably to predict and explain teleologically what it would do under a range of conditions…

I have been arguing that a grasp of the subjunctive background of an individual qua member of a kind is a condition on the grasp of that individual as a determinate thing. This raises the hypothesis that teleological vocabulary is used as a means of identifying, individuating, and understanding organisms as members of particular species or kinds. That hypothesis in turn predicts that there are evident patterns in the subjunctive backgrounds of organic things, and which can be appealed to as an explanation for the aptness of teleological talk. To exhibit these patterns is to lend support to that hypothesis. The rest of the essay is directed at this task.

5 Some desiderata of the account

Although there is no univocity over the details, there are a range of features of organisms that philosophers have typically thought emblematic of their apparent purposiveness. I focus on five.

Perhaps the most recurring theme is the persistence and plasticity of organic activity (Desmond & Huneman, 2020; Fulda, 2020; McShea, 2012; Nagel, 1977b; Sommerhoff, 1950; Walsh, 2012). The activities of the living thing tend toward the realization of its ends in a variety of different conditions (persistence), and those activities can be supplemented or substituted when facing potential defeaters (plasticity). These persistent and plastic processes underlie the organism’s existence as a thing that, as one might say, appropriates and wards off the causal forces of its environment, in general making use of some of those forces as means toward the ends of its existence, and staving off those that threaten the realization of its ends. Its purposes thereby form hierarchies of need, and we subsume our understanding of its activities under our conception of these needs (McShea, 2012, 2016a and 2016b, and Walsh, 2008): the stomata in ferns close at night so that water can be retained; water is retained so that, among other things, hydrogen is available for the synthesis of ATP; ATP is synthesized so that fuel is available for the process of cellular construction (among other things); etc. Along these hierarchies, individual processes are means toward both more distal ends, and toward processes that themselves successively contribute toward these ends. Through this activity, the parts of the organism are organized along pathways of homeostatic feedback and self-regulation (Bich et al., 2016, Mayr, 1974; Mossio & Bich, 2017; Nagel, 1977b; Walsh, 2008 and 2018). Qua organism, this organization is almost invariably oriented toward the survival and reproduction of the individual (Ayala, 1998; Corti, 2022; Mossio & Bich, 2017). Additionally, we distinguish the purposive activities internal to the organism from the nonpurposive activities that underlie and situate the organism’s activity in its environment (Fulda, 2017; Lee & McShea, 2020; McShea, 2012; Nagel, 1977b). Nitrogen-infused soil is beneficial to the growth of many plants, but it is not in general true that nitrogen is in the soil so that plants can grow. Similarly, though plants grow toward the sun so that photosynthesis can occur, it is not the case that sunlight shines on plants so that photosynthesis can occur.

I summarize these features as desiderata that a subjunctive account of the purposiveness of organic activity should be able to explain. My claim is not that their explanations are either individually necessary or jointly sufficient for any adequate account of organic purposiveness, but only that the ability to explain these features counts in favor of such an account.

Persistence and plasticity: How does the subjunctive background of organic development and growth account for the persistence and plasticity of these activities?

Hierarchies of need: How are the hierarchically organized purposes of the organism reflected in its subjunctive background?

Homeostatic self-regulation: How does the subjunctive background explain why talk of homeostatic organization and self-regulation is apt?

Survival and reproduction: How are individual survival and reproduction represented as preeminent organic ends in an organism’s subjunctive background?

Purposive and nonpurposive activity: How do we distinguish organic activity, as directed toward the satisfaction of organic purposes, from the nonpurposive environmental forces that are appropriated by the organism?

6 Organism-enabled subjunctive stabilities

In this section, I introduce a series of two-dimensional representations for the subjunctive background of organic generation and growth. The aim is to use subjunctive conditionals to give a (partial) characterization of the content of such attributions of purpose as “plants grow toward sunlight so that photosynthesis can occur” and “cellulose is synthesized at the plasma membrane so that new cells can be produced”. With Greek letters as schematic terms ranging over sentences, I represent the general form of such attributions as:

$$\upvarphi {\text{ so that }}\uppsi$$

Call the sentence in the first position the means and that in the second the end (making allowances for talk of activities and states as needed). The key notion is that of organism-enabled subjunctively stable relations (OESS relations) among different organic and inorganic activities and states (I will use “OESS” as a count noun as well, understood as denoting such relations—in such cases, read this as “organism-enabled subjunctive stability”). In an OESS relation between a means and an end, the organism and/or some of its organic subsystems feature as both agents and patients. That is, an OESS is a process or state in which the organism is acting, or has or will have acted, upon itself. Crucially, an OESS relation is characterized by defeasibility: just because there is an organism-enabled subjunctive stability between, e.g., photosynthesis and growth, it does not follow that every case of photosynthesis entails growth. And while the illustrating examples typically make use of biochemical details, the subjunctive stabilities can also be characterized in terms of macroscopically observable properties of the organism’s development and growth.

Where a given organism is under consideration, where φ and ψ concern activities and/or states in which the organism or some of its organic parts feature as both agents and patients, and where A, B range over sentences denoting events that affect the organism, the basic structure of an OESS relation between an internal means and an end is that of a relatively stable connection between the means and the end (see Fig. 1; and recall that “φ > ψ” is read “if it were to be that φ, then it would be that ψ”).¹⁵

Fig. 1

OESS peristence

Schematically, the persistence condition represents that the subjunctive relation between φ and ψ is robust under the influences of A, B, etc. Call the initial subjunctive the root of a given OESS. I will sometimes speak of the antecedent of a root subjunctive as a means, and the consequent as an end. This organism-enabled subjunctively stable relation between organic means and end corresponds to a persistence condition on the activities of the organism—e.g., in a variety of different situations the plant would grow toward the sunlight, and it would synthesize cellulose at the plasma membrane.

The realization of an end is not subjunctively robust under any supposition, however; for if the plant is early-on overcrowded by the plants surrounding it, then it will not have sufficient energy to grow toward the sunlight or to store the glucose needed for cellulose formation. Alongside persistence, a plasticity condition on organic activity is realized by feedback cycles where the defeat (D) of the realization of an end is circumvented by the actualization of another organic process that once again enables (E) that end (see Fig. 2; strictly speaking, the consequents might be specified as obtaining at times that are posterior to the times at which the antecedents obtain, and the occurrences of ψ as negated and as non-negated might be distinguished as two separate activities or events, but I suppress these details for ease of notation):

Fig. 2

OESS plasticity

The subjunctively stable relation between φ and ψ is plastic in that what would otherwise be a defeater D (of the tendency of φing to lead to ψ) is overcome by a subsidiary enabling process E that reinstates that relation.

Fig. 3

Condensed OESS

Consider a pepper plant and the growth of some one branch and leaf. If the pepper plant has been planted in a part of the garden that affords ample sunlight, the plant would see to it that the leaf grows in such-and-such a direction (which, as it happens, is to grow toward the sun). But if the pepper plant has been planted in a part of the garden that affords ample sunlight and a squash plant overcrowds it, then it is not the case that the plant would see to it that the leaf grows in that direction. But if the pepper plant has been planted in a part of the garden that affords ample sunlight and a squash plant overcrowds it, then the pepper plant would grow away and out from under the squash plant. And if the pepper plant has been planted in a part of the garden that affords ample sunlight, and a squash plant overcrowds it, and the pepper plant grows away from and out from under the squash plant, then the pepper plant’s leaf would grow toward the sun. The subjunctive background of the process of plant growth, having this persistent and plastic character, possesses a general structure found in various types of organic activity (for analogous reasons, it is often useful to think of organic generation and growth through the framework of agency—cf. the discussion of autonomous systems in Fulda, 2020, p. 323).¹⁶

The basic structure of an OESS can be represented as in Fig. 3 (focusing on the root and suppressing representation of the conditions of persistence in the absence of defeat). In the notation used below, this is the basic unit of an organism-enabled subjunctive stability, relating one means to a single end according to its conditions of persistence and plasticity.¹⁷ These means/end relations can be generalized along two axes: a vertical axis representing the variety of ends that a given means tends toward, and a horizontal axis representing the relationship between a given end and the successive ends it serves in turn as a means for.

Consider the cascade of effects that surround and follow chloroplast activation in photosynthesis in green plants (cf. Nobel, 2009, Chap. 4–6). When sunlight enters chloroplast organelles it passes into stacks of thylakoid cells, whose disc-like structures are coated with quantasomes, small particles with chlorophyll pigments. As sunlight strikes these particles, photosystem protein complexes funnel photons to reaction centers (specialized chlorophyl “traps” where photochemical reactions occur). Within these reaction centers, this energy is used, together with electrons produced from the splitting up of water molecules, to pump protons (in H⁺ ions) through the thylakoid membrane. This begins a process that has a proximal result in the creation of ATP (among other things), which is then shuttled around the plant, stored, and used in the various life-supporting activities typical for its species.

In this example, horizonal OESS relations can be seen in the way that a process like the funneling of photon energy into reaction centers in chloroplast organelles leads to a gradient flow of electrochemical energy used for ATP creation, while ATP creation contributes to (among other things) CO₂ capture, which in turn contributes to carbon fixation, which contributes to cellular growth at the root and shoot, etc. In each case, what is at one stage the end of a process (as ATP creation resulting from chlorophyll activation) becomes a means to a further end (as ATP production leads to CO₂ capture). Formally, this OESS relation is displayed in subjunctive conditionals where the consequent of one conditional is the antecedent of another, arrayed horizontally in the diagrams to follow (e.g., if ATP were created then CO₂ would be captured, and if CO₂ were captured then carbon would be fixated).

The vertical dimension of the diagrams below displays the variety of processes and states that any particular antecedent functions as a means toward. ATP creation is put to use for CO₂ capture and cellular growth at the root and shoot, but also cellular repair, the creation of new leaves, and the formation of flowers and fruit bodies. This vertical dimension is displayed in columns of OESSs which share a common antecedent in their roots (see Fig. 4).

Fig. 4

Neuron with two displayed OESSs

It is also convenient to note the more general ends that a particular means-end relation fosters. Though in general the satisfaction of local organic ends contributes to the satisfaction of other ends, some ends are more strongly correlated with the realization of certain local ends. To represent this fact, we need some way of marking that some subjunctive tendencies of a local process or set of processes are correlated with certain distal ends. This is useful because while some ends are both widely represented across the subjunctive background of every organism, they are not subjunctively robust under the satisfaction of every end. To see a vivid instance of this, consider the ends individual survival and reproduction, two ends prototypical of the living thing. In plant species that die shortly after fertilization occurs, the inhibition of flowering can aid in the survival of the individual—at least for a time. It is this feature that makes biennial plants like kale and collard greens, together with their hearty resistance to the cold (a subjunctive stability toward survival), so appealing to home gardeners: so long as you keep them from flowering, and so long as they’ve grown large enough to weather the first year, they produce edible material for 2 years. What this shows is that while individual survival and reproduction may be jointly subjunctively robust under many situations an organism faces, the two ends can come apart. And this suggests keeping track of which general ends are supported by which specific means.

Adopting the convention that a given mean’s relation to several more general ends be included as a subjunctive conditional displayed in bold, where multiple such conditionals are separated by semicolons, with a line inscribed underneath to indicate that a collection of OESSs with a common antecedent is being treated as a unit, and where “s” and “r” denote survival and reproduction (while “a” is a schematic term), the resulting collection of OESSs for a given antecedent means is displayed in Fig. 4.

Call such a collection of OESSs, all of whose roots share a common antecedent, and which include a specification (in bold at the bottom) of the general ends these OESSs foster in the organism, a neuron.

Note that not every neuron need have survival and reproduction represented in bold as general ends that a collection of OESSs serves. As the discussion of biennial plants indicates, sometimes individual survival is supported by processes that are owed to a failure to reproduce. I treat this use of bold as a notational device for ease of representing that particular states and processes are widespread across a subjunctive background, and the inclusion of survival and representation is meant to signal the extent to which these ends are characteristic of organic activity. In a more detailed rendering of a given subjunctive background, this convention might be replaced by darkening the font of widely represented sentences across an array, in effect picking a shade for the font that is weighted by the number of occurrences of the end (or via a proportional weighting) across the display. If arrays were grouped adjacent to one another, this would allow one to look out across a collection of arrays and see the ends typical of the species in question.

These structures are neuronal in that a network of relations branch out from them to other such structures. For in addition to the vertical dimension tracking a given mean’s place in subjunctive space, there is the place of a given means/end connection in the vital economy of the organism as a whole. This feature of the subjunctive background of the organism can be displayed in horizontal relations between individual OESSs along one vertical column, and successive neurons whose OESSs represent processes whose successful implementation depends upon the success of the process represented by that first OESS. This is displayed in Fig. 5 (note that the consequent of the root subjunctive conditional in the individual OESS at the upper left occurs in the antecedent of the subjunctive conditionals in each of the collection of OESSs of the neuron at the right). For simplicity of notation, I treat each OESS as having only a single axon connection to a successive neuron, where the consequent of the root subjunctive in the OESS is the antecedent of each OESS in that successive neuron. This in effect groups together all of the successive processes that the first OESS has the function of supporting. For some purposes, it may be useful to distinguish separate axon connections between a single OESS and distinct neurons, but I suppress that detail here.

Fig. 5

An array with two neurons, 3 OESSs, and an axon connection

Call such connections axon connections (I will refer to them as axons as well). Axon connections relate OESSs within one neuron to the groups of OESSs found in successive neurons that are subjunctively supported by that first OESS; note in particular that the consequent of the root subjunctive in the prior OESS occurs as antecedent in the root subjunctives of all of the OESSs of the successive neuron. Call such displays of OESSs, neurons, and axons an array.

Fig. 6

Slice of a psyche (organic subjunctive background) with vertical intraneuronal and horizontal interneuronal structure explained

As with the use of bold font to mark general tendencies supported by the OESSs of a given neuron, and a line beneath those tendencies to mark divisions between neurons, the arrow and the bracket are notational devices. Using the above array as an illustration, the arrow and bracket signify that, within one (left) neuron whose OESSs all have roots with φ as an antecedent, one such OESS, rooted in φ > ψ, is subjunctively stable toward some consequent condition ψ (an end) that is in turn an antecedent condition (a means) in the roots of the OESSs for a different (right) neuron, in virtue of which the OESS in the left neuron bears an axon connection to the right neuron. While the arrow and bracket assist in displaying axon connections between individual OESSs and successive neurons, those connections are defined in terms of relations between OESSs and neurons without regard for the notation.¹⁸

The basic two-dimensional structure of OESS relations is constituted by a single vertical and a single horizontal path from an OESS represented in the upper-left portion of an array. Call this upper-left OESS the node of such an array (whether an OESS is a node is, for all I have said, an artifact of the way an array is displayed; in the array in Fig. 5, each of the OESSs rooted in ψ > ρ and in φ > χ could just as well be OESS nodes for different arrays). Successive OESSs along the vertical dimension of an array, within individual neurons, articulate how the antecedents of those OESSs are related to other organic processes. Successive OESSs along the horizontal dimension, from neuron to neuron, articulate how a local means-end subjunctive relation is hierarchically related to other OESSs, via the (defeasible) transitivity of the subjunctive conditional. See Fig. 6 for an illustration.

Notice that in Fig. 6 there is a single neuron with two OESSs displayed in the left column of the array, two distinct neurons in the central column (one whose OESSs are rooted in subjunctives with ψ as an antecedent, and the other with OESSs rooted in subjunctives with χ as an antecedent), and a single neuron with a single displayed OESS in the right column. The branching axon connections from the two neurons in the central columns indicates that, in general, multiple OESSs within any given neuron will have axon connections to other successive neurons in an array (this is also displayed with the two OESSs in the leftmost neuron, with two displayed axon connections).¹⁹ Tracking these relations requires representing additional OESSs within individual neurons, and specifying the axon connections between them and successive neurons. Call an array with such structure a slice, and call an array plotting only the vertical and horizontal connections from its node (as in Fig. 5) a simple array.²⁰

The term “slice” is meant to evoke that a single such array communicates only the information consequent on selection of a particular node OESS, its neuron, the axon connections between that neuron and successive neurons, and among successive OESSs and neurons. The information needed to give a tolerably accurate picture of the teleological modal profile of an organism requires considering groups of slices, each with a different node. This would allow for additional structure to be imposed, in that axons might relate OESSs in the neurons of one slice to neurons in other slices, perhaps in cases where a given end is supported by different means. For in general, individual ends will be supported by the subjunctive stabilities of a number of means—ATP production tends toward cellular growth, but only in a context in which water is retained for hydrolysis so that the energy stored in ATP molecules can be used.

In one slice, for instance, an OESS rooted in φ > ψ represents φ is a means to ψ; but in another slice, an OESS rooted in χ > ψ represents χ as a means to ψ. And so it may be that the OESS in the first slice bears an axon connection to neurons in the other slice with OESSs rooted in subjunctives with ψ as their antecedents. Consequently, in cases where two slices include neurons with OESSs rooted in subjunctives whose antecedents are jointly conducive toward the satisfaction of some end, it might be useful to represent intermediate slices whose neurons contain OESSs rooted in subjunctives whose antecedents are conjunctions of the individual antecedents of the other two slices—e.g., φ&χ > ψ as the root of an OESS in a neuron on a slice intermediate between a slice containing a neuron with an OESS rooted in φ > ψ, and a slice containing a neuron with an OESS rooted in χ > ψ. This sort of cross-slice relationship might be mapped even in cases where the individual ends (the consequents of the subjunctives in question) differ. For instance, where φ > ψ is the root of an OESS in a neuron of one slice, and χ > τ the root of an OESS in a neuron of another slice, and where the activities denoted by φ and χ jointly tend toward an end denoted by θ, there might be a third slice that contains a neuron with an OESS rooted in φ&χ > θ. In other cases, disjunctive antecedents might be used as well.

Considering only individual slices, their neurons, and their axon connections, more detail could be added still. Feedback cycles in organic behavior will transpose individual OESS units across both the vertical and horizontal dimensions, with the antecedents φ of root subjunctives in some OESSs having axon relations to neurons (or their successors) whose OESSs have root subjunctives with φ as a consequent: what is at one stage a means to a proximal end may eventually become a means to itself (or its kind of activity) as a distal end. For the most part, I suppress these permutations in what follows and focus on the linear and acyclic character of organic processes as they recur across individual slices.

Call the set of slices typifying a given organism a psyche of that organism. We can now give a more precise characterization of the subjunctive background characteristic of an organism, by saying that it has the structure of a psyche. The term “psyche” is of course meant to echo Aristotle’s use of ψυχή as a label for the form of a living thing, such that it makes sense to speak of the psyche or soul of a plant (as did Aristotle). But this is not meant to imply that purposiveness is always a matter of cognition, as the term “psyche” might seem to imply today, and having introduced the notion here I set a discussion of psyches aside for now (although see Linson & Calvo, 2020, Maher, 2017, and Thompson, 2007 for extended defenses of the assimilation of cognition to organic activity in general).

7 Satisfying the desiderata

The first two desiderata for analysis that a subjunctive background can be expected to meet were conditions of persistence and plasticity on organic development and growth, illustrated in the discussion of Figs. 1 and 2 of the last section. The next three desiderata can now be addressed:

Hierarchies of need: How are the hierarchically organized purposes of the organism reflected in its subjunctive background?

Homeostatic self-regulation: How does the subjunctive background explain why talk of homeostatic organization and self-regulation is apt?

Survival and reproduction: How are individual survival and reproduction represented as preeminent organic ends in an organism’s subjunctive background?

The hierarchical character of the purposive organization of a living thing, where activities of means that are more causally distal from a given end support intermediate means that successively contribute to that end, is embodied in hypothetical syllogisms (from φ > ψ and ψ > χ, infer φ > χ) drawn horizontally across axons in the subjunctive background. One of the things that ATP creation allows for is cellular growth, which in turn tends the plant toward exposure to the sun. And so, generally or for the most part, we navigate this material-inferential space by drawing the transitive implication that ATP creation tends toward the plant’s exposure to the sun.

The processes operating between ATP production and cellular growth, and between cellular growth and exposure to the sun, involve further intermediaries: ATP needs to be released at or transported to the growth site, and cellular construction needs to be responsive to obstructions like an overcrowding squash plant. These considerations illustrate the fact that, as we frame a view on what the plant is up to, we find ourselves organizing its activities under a conception of a hierarchy of means-end relations with a recursive or fractal-like structure: within those means-end relations that relate activities of the whole organism, we find additional means-end relations among the organism’s parts, organized according to collective ends for the individual’s continued existence and reproduction (I have said next to nothing of the use of proteins in the coordination of cellular processes, for instance). That hierarchy is represented in the transitivity of the subjunctive conditionals that mark the horizontal dimension of the psyche or subjunctive background of the organism. These patterns in the subjunctive background of organic activity, individuated in terms of shared antecedents and consequents in axon connections across that background, specify intermediate means/end relations that mediate the successful integration of more distal organic processes into a general form of life.²¹

Another type of pattern evident in this background is marked out in positive and negative feedback cycles across the organism’s typical states and activities, tending toward the ends characteristic of its kind. These feedback cycles represent aspects of the homeostatic self-regulation of organic activity: were ATP produced the plant would fuel shoot apical meristem growth, were shoot apical meristem growth to occur the plant would capture more sunlight, and were the plant to capture more sunlight more ATP would be produced by the plant; thus, for the most part, were ATP produced by the plant then more ATP would be produced by the plant. Talk of homeostatic self-regulation is in general apt, then, because these hierarchical subjunctive stabilities collectively generate the ongoing survival and reproduction of the individual. In the face of a need for ATP to fuel growth, ATP would be created and distributed through the system across a range of conditions. The specific subjunctives we accept, and their conditions of defeat, articulate our understanding of the individual as one of its kind. At the level of detail presently under discussion, the kind is something like green plant (or autotrophic plant). But whatever the category, we understand the living thing to exhibit homeostatic self-regulation in its tendencies to use the environment to sustain its ongoing existence, in a way characteristic of the kind of organism in question.

In order to account for the preeminence of the ends of survival and reproduction in our understanding of the organism, notice that at each stage of this hierarchy there are, in addition to local subjunctively stable relations between means and ends, more general stabilities that recur across the organism’s processes. When asked why the pepper plant looks so withered, we explain that it was not able to take advantage of the sunlight it needs to flourish, owing to the growth of the squash beside it. The failure of sufficient sunlight will likewise explain (in part) why the plant never produced flowers or fruit, why its roots are so poorly developed, etc. In terms of notation, this representation is achieved by the use of bold in the two-dimensional graphs that represent an organism’s psyche, and which I have displayed at the bottom of individual neurons—one glances across the graph (slice) of an organism’s subjunctive background (psyche) to read the ends that are characteristic of its kind (although again, it is possible to represent this recurrence by other means, e.g. via a weighted shading of a dispayed subjunctive in terms of how frequently it appears in a psyche). Survival and reproduction will occur as ends across these slices, and these ends are preeminent in our understanding of organisms precisely because it is they which recur again and again across the explanatory hierarchies that govern our understanding of individual organic things.

The fifth desideratum was:

Purposive and nonpurposive activity: How do we distinguish organic activity, as directed toward the satisfaction of organic purposes, from the nonpurposive environmental forces that are appropriated by the organism?

The task is to give some principled reason for ruling out as infelicitous judgments like “sunlight shines on plants so that photosynthesis can occur” and “nitrogen is present in soil so that plants can fuel their growth”, even though such activities do tend toward the corresponding results. Relatedly, there is the question of where, and on what basis, to draw a distinction between the teleological activity of living things and the non-teleological behavior of the inanimate world—e.g., does the movement of a bacterium up a chemical gradient count as purposive?

Taking the second issue first, I see no reason to think we require a fixed line (or a set of necessary and sufficient conditions) distinguishing teleological from non-teleological activity, in order to profitably investigate the relations involved in (our cognition of) characteristically or paradigmatically teleological activity. Lee & McShea, (2020), for instance, operationalize the goal-directed behavior of bacteria movement, explaining it in terms of its persistence and plasticity. But so far as it goes, this leaves open that weather patterns or other non-organic processes might exhibit goal-directedness in this sense, and they conclude that goal-directed and non-goal-directed behavior lie on a continuum (cf. the closing paragraph of McShea, 2016a, and the closing paragraph of Cummins, 1975). Similarly, while Fulda, (2017) outlines an account of organic purposiveness that appeals to the categories of agency, he advocates allowing that “there can be degrees of agency along a continuum, from the simplest adaptive agents at one extreme, such as bacteria, to the most sophisticated cognitive agents on the other, such as human beings” (p. 70). As Walsh points out in his own agential characterization of purposive activity (2018, p. 171; and see the discussion in Sect. 17.4 of Uller, 2023):

Understanding these new phenomena calls, in turn, for special theoretical concepts that are not required to account for domains in which these configurations do not occur.

We may benefit from a study of such concepts even if we do not define them in terms of a set of necessary and sufficient conditions, and even if we suppose that their instances lie on a continuum with the clearly non-purposive at the other extreme.

All the same, there are felicitous and infelicitous uses of teleological language. Recall that teleological claims about organisms are explanatory. To be told that the bacterium is moving in a particular direction in order to reach a food source is to be given a means of anticipating the bacterium’s behavior in a variety of subjunctive conditions. This in turn helps us understand why the bacterium might take a sudden turn were one to jostle the solution it is suspended in.

Against this background, notice that there is nothing about the satisfaction of the putative ends of photosynthesis or plant growth that explains why the sun shines or why nitrogen is in the soil. In these cases, the putative end is not explanatory of the putative means; and there is no reason to think, were sunlight no longer to fall on plants, that the sun would start doing something different. But such a relationship is a hallmark of teleological explanation. The absence of that explanatory relation is in turn exhibited in the fact that were there to be no photosynthetic activity or plant growth, there still would be a shining sun and nitrogen in the soil. This suggests that where there is no stage in the activities of the organism that leads to some putative means as an end of its other activities, there is no explanatory relation between the putative means and its putative end, and so there is no question of that putative means as a genuine means. That putative means may be a causal precondition on the purposive activities of the organism, a link in a chain of powers or processes the organism appropriates for its own ends, but the organism is not itself purposively directing that precondition.

Finally, consider the following two claims:

plants need to retain rainwater in order to fuel photosynthesis

rainwater needs to fall on plants in order to fuel photosynthesis

Although each is felicitous, only the second remains felicitous when the need modality is removed (and the corresponding grammatical adjustments made; the hashtag indicates an infelicitous expression):

plants retain rainwater in order to fuel photosynthesis

# rainwater falls on plants in order to fuel photosynthesis

This is because the first claim speaks of a self-directed activity of a plant, whereas the second only concerns a process that, while necessary for the plant’s survival, is not part of its own activity. This goes some way toward explaining why a marble rolling around the inside of a bowl, coming to settle in the bottom despite the possibility of having its trajectory gently disturbed in any number of ways, is not a purposive process. For the marble is not, as so described, doing anything that could be characterized as right or wrong (or otherwise warrants the use of evaluative language), and this in turn is coordinate with the fact that the marble’s movement is not part of the bowl-plus-marble system’s identity conditions. Rather, that process is the consequence of relations governing a much wider class of objects: namely, massive things in gravitational and mechanical interaction.²²

8 On the differentiation and unification of the living thing, with two applications

With the formal details in place, I turn now to some applications of this analysis, in the interest of exhibiting its usefulness in articulating the subjunctive or material-inferential structure of (our understanding of) the organic world.

It is common to find homologous organs (parts) performing similar roles in different species, though the subjunctive space of an organ varies from species to species. And because the processes that underlie the growth and use of, e.g., visual organs in animals are similar for a wide range of species, differences in the ways those processes play out in the lives of organisms contribute to differences concerning what it is to be a member of a given species. These variations represent different forms of life, ways of flourishing in the world that are peculiar to a species (or some less general kind-classification). Imposing a bit of structure on this picture, we can say that the processes of differentiation that mark off the subsystems of an organism from the subsystems of other organisms only tell half the story. It is just as important that we have a sense of the way in which those differentiated processes are unified in the form of life characteristic of the kind in question.

Consider the case of ATP production in glycolysis, a form of cellular respiration common in many species (both plants and animals). The six-carbon sugar molecule glucose is generally stable, and so the formation of sugars by an organism allow the organism to store energy in that form. During glycolysis, that stored energy is released. Two ATP molecules each donate a phosphate group to the sugar molecule, resulting in two ADP (adenosine diphosphate) and a fructose bi-phosphate molecule. Additional enzymes then split this fructose molecule into two three-carbon sugar molecules that are afterward broken down to produce four ATP molecules and two NADH (nicotinamide adenine dinucleotide plus hydrogen) molecules, resulting in a net gain of two ATP (along with two NADH). As ATP is a major source of molecular energy, reservoirs of sugar are able to be converted to sources of energy by this process.

This self-regulating process in the use of ATP is common across many species, but different kinds of species accomplish it in different ways. That is to say, the production of ATP through glycolysis is a structure of differentiation (a feature of organic activity that characterizes how an organism maintains itself) that is common across many organisms, but which is differently unified in the production of specific traits that vary from organism to organism. While animals form ATP only in the mitochondria of their cells, green plants synthesize ATP through photosynthesis. Furthermore, different environmental conditions support and inhibit photosynthesis in different ways for different kinds of plant, and similar processes of differentiation are unified in ways that characterize those kinds.

Cacti and ferns, for instance, each possess stomata—pores that open and close on the surface of a plant so as to regulate the inflow and outflow of water, carbon dioxide, and oxygen. In ferns, stomata close at night so that water is retained for hydrolysis in the breakdown of ATP, whereas stomata are open in the day so that CO₂ can be used (via a diffusion gradient) to fuel photosynthesis. Some water is released during this diurnal process, but ferns live in environments where that loss is not important. In cacti, by contrast, open stomata during the day would lead to the release of excess water to the detriment of the plant, and so stomata are closed during the day in order to retain water. CO₂ capturing is instead a nocturnal activity. That CO₂ is then converted with the enzyme PEP (phosphoenolpyruvate) carboxylase, or PEPC, into a form that is stored so that, during the day, it can be used to power photosynthesis.²³

The energy available in ATP is appropriated for the construction of different cellular structures in these two species as well. It is generally thought that cacti have barbs so that predators will be deterred from eating them, for in the water-scarce environments in which cacti grow they would otherwise be sources of hydration for animals.²⁴ But ferns do not thrive in water-scarce environments and so they do not need to produce such structures. And despite these differences, in both kinds of plant ATP fuels the development of chloroplasts that are locations for the photosynthetic creation of further ATP, as well as sites for the biosynthesis of fatty and amino acids. These processes are unified in ways that are specific to the two kinds, however. Photosynthesis in ferns is fueled by the creation of chloroplast-packed fronds that spread out from the plant body, whereas photosynthesis in cacti takes place through chloroplasts in the plant body. And fatty and amino acid biosynthesis in general requires PEP use in chloroplasts, but in cacti there is the additional need for PEPC noted above.²⁵ Finally, it is worth noting that animals use ATP in nervous system signaling and development, although it must be synthesized by mitochondria.

Together, these considerations help illustrate some of the large-scale structure of (our subjunctive reasoning about) organic purposes. This structure materially conditions our understanding of cacti and ferns as plants whose diverse parts work together toward, or are unified in the pursuit of, the ends characteristic of their kinds. To see this, consider the partial representation of these two sets of processes in the slices of the psyches (organic subjunctive backgrounds) of cacti and ferns displayed in Figs. 7 and 8. For simplicity, in these figures only the root subjunctives of individual OESSs are displayed, only the general ends associated with individual neurons are given in bold (as opposed to the subjunctive conditionals that have those ends as consequents), and only those general ends that illustrate the foregoing discussion are listed (the general ends of survival and reproduction, for instance, are omitted here).

Fig. 7

Slice of the psyche (organic subjunctive background) of a cactus

Fig. 8

Slice of the psyche (organic subjunctive background) of a fern

Not only are there differences in the differentiations of these two forms of organism with distinct evolutionary trajectories (as exhibited by the fact that only the cactus tends toward the production of PEPC as a means of storing CO₂), but also in their unifications. This is represented by the fact that, even though both kinds of organism tend toward the production of stomata and ATP, this structure and substance are used by them in different ways—the diurnal capture and use of CO₂, and the use of ATP to form fronds with chloroplasts in them, is emblematic of the fern, while the nocturnal capture and storage of CO₂ for diurnal photosynthesis, and the use of ATP to form barbs and chloroplasts in the plant body, is emblematic of the cactus.

Though framed with respect to plant life, the view applies just as well to the development and growth of animals. Comparison of the visual systems in gazelle and cheetah presents another case where similar processes of differentiation are unified according to specific forms of life. The production and use of opsins (proteins for vision) indicate vision is an end of these processes in both gazelle and cheetah, though that end is integrated with the rest of the activity characteristic of the species in different ways. While the eyes of the cheetah and the gazelle are both subjunctively stable in the realization of sharp vision and movement tracking, the placement of the eyes on the side of the head affords the gazelle better chance to see predators, whereas the placement of the cheetah’s eyes on the front of its head enable it to better gauge distance in chasing its prey. And though the biochemical processes of muscular development are similar in both animals, the interaction between such things as the sight of a given animal, adrenaline production, and muscle response contribute to different tendencies (think of “flight” and “fight” responses). Again, common structures in the differentiation of the processes characteristic of many organic kinds are unified in ways that are peculiar to separate kinds. And again, while the biochemical detail of these processes affords a more fine-grained understanding of their operation, their large-scale subjunctive structure is evident even in the absence of an awareness of that detail.

9 Conclusion

I have offered a formal framework for representing the teleological fine-structure of large-scale organic activity in terms of two-dimensional arrays of subjunctive conditionals, and I have argued that this formalism does tolerably well in accounting for some of the paradigmatically purposive features of living things. While I have occasionally referenced related views in the philosophy of biology, and while I discussed different ways of semantically interpreting subjunctive conditionals, I have presented the framework as a formalism suitable for use in a range of research programs.

Consider, for instance, that it may be possible to devise a computer program capable of investigating whether such formal structures appear in databases containting collections of subjunctive conditionals characterizing different physical systems. If that is so, one might look for the signs of organic processes in what otherwise seem to be merely physical systems. The case of photosynthesis in autotrophic plants indicates one such possible application. Suppose a group of researchers otherwise unaware of the life-supporting role of photosynthesis is given information—encoded in a database of subjunctive conditionals—about the way photons are funneled into reaction centers on leaves, transmitted into thylakoid cells, and used to pump protons through the thylakoid membrane. Insofar as these activities exhibit the subjunctive structure found in slices of psyches, it seems possible to use the presence of such structure to predict that these processes are part of the life-sustaining activities of green plants. Just so, in cases where we do not already possess this understanding, it may be possible to use this formalism to investigate whether other seemingly non-organic systems exhibit the hallmarks of organic goal-directedness.

Toward the end of general application, throughout the essay I have illustrated that a joint proof-theoretic/deontic and model-theoretic/ontic interpretation of the formalism is possible, the one in terms of rules of inference and the other in terms of a sphere of spatio-termporal subjunctive possibilities. This position is meant to give the framework a more universal application, and to help illustrate the depth of view afforded by these two complementary perspectives. On one hand, to be in cognitive truck with an organism qua organism is to reason about it according to subjunctive patterns of the sort detailed above. Talk of the purpose of some organic activity is talk that facilitates this cognition by guiding an auditor in reasoning about how an organism would behave in various contexts. On the other hand—in virtue of the way our thought is responsive to facts about organic activity—thinking in patterns like those introduced here enables our understanding of organisms as the kinds of thing they are. Consequently, this two-dimensional representation of the psyches or subjunctive backgrounds of organic activity offers the prospect of developing a formally tractable framework both for modelling the purposive character of the organic world, and for modelling the cognitive processes that constitute or contribute toward our understanding of that world.